Johnson solids

We wondered last week why our shelves are not hexagonal, like the cells of bees, rather than rectangular (ortoédricas, to be exact). Are the bees smarter than us, by building a structurally more resilient type of "shelving" that is a clear material saving? The "pact with nature" that Le Corbusier saw in the right angle is the explanation. We are big and heavy beings (compared to the bees), much more dependent on the horizontal-vertical binomial, and we stack things (bricks, boxes); Not to mention the books, small ortoedros that we keep on shelves equally ortoédricas.

Sólidos de Johnson

For the same reason, explicit and obvious straight lines are more abundant in human works than in nature, followed closely by the circumferences (suffice to think of the ubiquitous wheels) and their bows.

And speaking of straight lines and arches of circumference, we have a clear example of his struggle (never better) as Queens of Design in Swords: The Westerners, historically, have been preferably straight, while in the orient were abundant curves, as the Arab Cutlass or the Japanese katana. But can we assure, without being experts in white weapons, that the blade of a katana is an arc of girth? Could it be another kind of curve that is more suitable for cutting heads? What singular property shares a circumference arc with a rectilinear segment? What other line can we include in this small group?

Illustrious polyhedra

Some readers have commented that the escutoide is not properly a new type of polyhedron (see comments from last week), but, in any case, a new natural geometric object. They do not lack reason, although that does not subtract a shred of interest from the discovery. Polyhedra, as we have seen, are classified according to certain regularities that make them singular, the more singular the stricter these regularities are. The most outstanding, as we have seen in previous deliveries, are the five Platonic solids, regular and convex polyhedra, followed by the solids Archimedean, those of Kepler-Poinsot and those of Catalan.

To complete the cast of illustrious polyhedra, we must mention Johnson's solids, the less demanding and, consequently, the most abundant. Johnson solids are convex polyhedra whose faces are regular polygons not all of the same type (then they would be platonic) combined in any way and in any proportion. For example, a pyramid like those of Egypt, square-based and whose side faces are equilateral triangles, is a Johnson solid (the first of the list, in fact, since they are classified from less to more complex).

Given the scarce conditions required to enter his club, one might think that there are innumerable Johnson solids; However, there are only 92, from the simple square pyramid to the unpronounceable triangular Hebesfenorrotonda. As usual, I invite my sagacious readers to take an analytical walk through the pantheon of these interesting polyhedra. and to share their reflections.